#Slughorn also wanted their discussion of Horcruxes kept secret.
Slughorn also wanted their discussion of Horcruxes kept secret.
When the Dark Lord asked Slughorn about Horcruxes, Slughorn told him to keep it quiet - Slughorn didn’t want anyone finding out that they’d talked about Horcruxes any more than he did.
“Of course,’ he muttered, ‘this is all hypothetical, what we’re discussing, isn’t it? All academic …’
‘Yes, sir, of course,’ said Riddle quickly.
‘But all the same, Tom … keep it quiet, what I’ve told – that’s to say, what we’ve discussed. People wouldn’t like to think we’ve been chatting about Horcruxes. It’s a banned subject at Hogwarts, you know … Dumbledore’s particularly fierce about it …”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
Knowing this, the Dark Lord would see no reason to kill Slughorn. Slughorn wasn’t a danger - he wanted the Horcrux conversation kept a secret just as much. When Harry tried finding out, Slughorn didn’t willingly tell him, and very much denied everything to do with the conversation.
“Sir,’ said Harry desperately, ‘I just thought there might be a bit more to the memory –’
‘Did you?’ said Slughorn. ‘Then you were wrong, weren’t you? WRONG!”
- Harry Potter and the Half-Blood Prince, Chapter 18 (Birthday Surprises)
The only reason Harry was able to get the information from Slughorn was his use of Felix Felicis, and only Dumbledore knew Slughorn would even have information. From what the Dark Lord knew, there was really no reason to kill Slughorn - it would be unnecessary and not very useful.